Finite Group Databasebeta

← Group #13147799

Character table — Group #13147799

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12223446664412121212121233666666121212123666121212121212121212121212121212121212121212124444222444444412121212121212126661212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-11-11-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-11-1-1-11-1-1-1-1-1-1-1-11-1-1111-1-1
χ51111111111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-1-1-11-111111-1-1-1-111-11-1-11-1
χ61111111111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-11-1-11-11111-1-1-1-1-1-11-111-11
χ71111111111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111-11-1-1111-1
χ81111111111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-111-1-1-1-111111-111-1-1-11
χ911111-1-11111-1-1-111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1111-1-1-11-111-1-111-1-111-1-11-1-11
χ1011111-1-11111-1-1-111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-1-111-11-1111-1-111-1-1-1-111-111-1
χ1111111-1-11111-1-1-111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-111-11-11-11-11
χ1211111-1-11111-1-1-111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1111-1-111-1-1-1-111-1-1111-11-11-11-1
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-111-1-1-1-111111-1-11-1-1
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1111111-1-1-1-111-1-1-111-111
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-111-1-1-1-11-1-11111-1-1-11111-1-1-1
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-111-111-1-1-11111-1-11-1-1-1-1111
χ172222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100002200000220000000000-1-1000-1-1
χ182222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-200000-2-200000000001100011
χ19222222222222222222-12-122-1-12-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000202000-1-1-1-1-1-1-1-100000000
χ20222222222222222222-12-122-1-12-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-20-20001111111100000000
χ212222222222-2-222-2-2-2-22-12-1-122-12222-1-1-1-1-1-111-2-2-2-211-1-1-1-11111111100002-2000002-20000000000-11000-11
χ222222222222-2-222-2-2-2-22-12-1-122-12222-1-1-1-1-1-111-2-2-2-211-1-1-1-1111111110000-2200000-2200000000001-10001-1
χ232222222222-2-222-2-2-2-2-12-122-1-12-1-1-1-1-1-1-1-122-2-21111-2-2-1-1-1-11111111122220000-20-2000-1-1-1-1111100000000
χ242222222222-2-222-2-2-2-2-12-122-1-12-1-1-1-1-1-1-1-122-2-21111-2-2-1-1-1-111111111-2-2-2-200002020001111-1-1-1-100000000
χ2522222-2-22222-2-2-222-2-22-12-1-122-1-2-2-2-2-1-1-1-111-1-122-2-2111111-1-1-1-1111100002-200000-220000000000-110001-1
χ2622222-2-22222-2-2-222-2-22-12-1-122-1-2-2-2-2-1-1-1-111-1-122-2-2111111-1-1-1-111110000-22000002-200000000001-1000-11
χ2722222-2-22222-2-2-222-2-2-12-122-1-121111-1-1-1-1-2-222-1-111-2-21111-1-1-1-1111122-2-2000020-2000-1-111-1-11100000000
χ2822222-2-22222-2-2-222-2-2-12-122-1-121111-1-1-1-1-2-222-1-111-2-21111-1-1-1-11111-2-2220000-20200011-1-111-1-100000000
χ2922222-2-2222-22-2-2-2-2222-12-1-122-1-2-2-2-2-1-1-1-11111-2-222-1-111111111-1-1-1-100002200000-2-20000000000-1-100011
χ3022222-2-2222-22-2-2-2-2222-12-1-122-1-2-2-2-2-1-1-1-11111-2-222-1-111111111-1-1-1-10000-2-20000022000000000011000-1-1
χ3122222-2-2222-22-2-2-2-222-12-122-1-121111-1-1-1-1-2-2-2-211-1-12211111111-1-1-1-122-2-20000-202000-1-11111-1-100000000
χ3222222-2-2222-22-2-2-2-222-12-122-1-121111-1-1-1-1-2-2-2-211-1-12211111111-1-1-1-1-2-222000020-200011-1-1-1-11100000000
χ332-22-222i−2i2-2-2002i−2i000022-22-22-2-22i2i−2i−2i22-2-22i−2i000000002i2i−2i−2i000000002-22i−2i00000000002-22i−2i000000000000
χ342-22-222i−2i2-2-2002i−2i000022-22-22-2-22i2i−2i−2i22-2-22i−2i000000002i2i−2i−2i00000000-22−2i2i0000000000-22−2i2i000000000000
χ352-22-222i−2i2-2-2002i−2i0000-1212-2-11-2−i−iii-1-1112i−2i00−i3i33−300−i−iii−i3−i3i3i333−3−32-22i−2i0000000000-11−ii−i3i33−300000000
χ362-22-222i−2i2-2-2002i−2i0000-1212-2-11-2−i−iii-1-1112i−2i00−i3i33−300−i−iii−i3−i3i3i333−3−3-22−2i2i00000000001-1i−ii3−i3−3300000000
χ372-22-222i−2i2-2-2002i−2i0000-1212-2-11-2−i−iii-1-1112i−2i00i3−i3−3300−i−iiii3i3−i3−i3−3−3332-22i−2i0000000000-11−iii3−i3−3300000000
χ382-22-222i−2i2-2-2002i−2i0000-1212-2-11-2−i−iii-1-1112i−2i00i3−i3−3300−i−iiii3i3−i3−i3−3−333-22−2i2i00000000001-1i−i−i3i33−300000000
χ392-22-22−2i2i2-2-200−2i2i000022-22-22-2-2−2i−2i2i2i22-2-2−2i2i00000000−2i−2i2i2i000000002-2−2i2i00000000002-2−2i2i000000000000
χ402-22-22−2i2i2-2-200−2i2i000022-22-22-2-2−2i−2i2i2i22-2-2−2i2i00000000−2i−2i2i2i00000000-222i−2i0000000000-222i−2i000000000000
χ412-22-22−2i2i2-2-200−2i2i0000-1212-2-11-2ii−i−i-1-111−2i2i00−i3i3−3300ii−i−i−i3−i3i3i3−3−3332-2−2i2i0000000000-11i−i−i3i3−3300000000
χ422-22-22−2i2i2-2-200−2i2i0000-1212-2-11-2ii−i−i-1-111−2i2i00−i3i3−3300ii−i−i−i3−i3i3i3−3−333-222i−2i00000000001-1−iii3−i33−300000000
χ432-22-22−2i2i2-2-200−2i2i0000-1212-2-11-2ii−i−i-1-111−2i2i00i3−i33−300ii−i−ii3i3−i3−i333−3−32-2−2i2i0000000000-11i−ii3−i33−300000000
χ442-22-22−2i2i2-2-200−2i2i0000-1212-2-11-2ii−i−i-1-111−2i2i00i3−i33−300ii−i−ii3i3−i3−i333−3−3-222i−2i00000000001-1−ii−i3i3−3300000000
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-2-2222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4744444-4-44444-4-4-444-4-4-2-2-2-2-2-2-2-22222111122-2-2-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4844444-4-4444-44-4-4-4-444-2-2-2-2-2-2-2-222221111222222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4944-4-4400-44-400000000444-44-4-4-400004-44-40000000000000000000000000000000000000000000000000000
χ5044-4-4400-44-4000000004-242-2-4-420000-22-220023−23000000000023−2323−230000000000000000000000000000000000
χ5144-4-4400-44-4000000004-242-2-4-420000-22-2200−23230000000000−2323−23230000000000000000000000000000000000
χ5244-4-4400-44-400000000-24-2-4422-4−2i32i3−2i32i3-22-220000000000−2i32i3−2i32i300000000000000000000000000000000000000
χ5344-4-4400-44-400000000-24-2-4422-42i3−2i32i3−2i3-22-2200000000002i3−2i32i3−2i300000000000000000000000000000000000000
χ5444-4-4400-44-400000000-2-2-22-2222−2i32i3−2i32i31-11-10023−23000000i3−i3i3−i3−33−333i−3i3i−3i000000000000000000000000000000
χ5544-4-4400-44-400000000-2-2-22-2222−2i32i3−2i32i31-11-100−2323000000i3−i3i3−i33−33−3−3i3i−3i3i000000000000000000000000000000
χ5644-4-4400-44-400000000-2-2-22-22222i3−2i32i3−2i31-11-10023−23000000−i3i3−i3i3−33−33−3i3i−3i3i000000000000000000000000000000
χ5744-4-4400-44-400000000-2-2-22-22222i3−2i32i3−2i31-11-100−2323000000−i3i3−i3i33−33−33i−3i3i−3i000000000000000000000000000000
χ584-44-444i−4i4-4-4004i−4i00004-2-4-224-424i4i−4i−4i-2-222−2i2i00000000−2i−2i2i2i00000000000000000000000000000000000000
χ594-44-444i−4i4-4-4004i−4i0000-2-22-22-222−2i−2i2i2i11-1-1−2i2i00−2i32i323−2300ii−i−ii3i3−i3−i3−3−333000000000000000000000000000000
χ604-44-444i−4i4-4-4004i−4i0000-2-22-22-222−2i−2i2i2i11-1-1−2i2i002i3−2i3−232300ii−i−i−i3−i3i3i333−3−3000000000000000000000000000000
χ614-44-44−4i4i4-4-400−4i4i00004-2-4-224-42−4i−4i4i4i-2-2222i−2i000000002i2i−2i−2i00000000000000000000000000000000000000
χ624-44-44−4i4i4-4-400−4i4i0000-2-22-22-2222i2i−2i−2i11-1-12i−2i00−2i32i3−232300−i−iiii3i3−i3−i333−3−3000000000000000000000000000000
χ634-44-44−4i4i4-4-400−4i4i0000-2-22-22-2222i2i−2i−2i11-1-12i−2i002i3−2i323−2300−i−iii−i3−i3i3i3−3−333000000000000000000000000000000
χ644-4-44400-4-440000000044-4-4-4-44400004-4-440000000000000000000000000000000000000000000000000000
χ654-4-44400-4-44000000004-2-422-44-20000-222-200000000−2i32i300000000−2i32i32i3−2i3000000000000000000000000000000
χ664-4-44400-4-44000000004-2-422-44-20000-222-2000000002i3−2i3000000002i3−2i3−2i32i3000000000000000000000000000000
χ674-4-44400-4-4400000000-242-4-42-2423−23−2323-222-2000000000023−23−232300000000000000000000000000000000000000
χ684-4-44400-4-4400000000-242-4-42-24−232323−23-222-20000000000−232323−2300000000000000000000000000000000000000
χ694-4-44400-4-4400000000-2-22222-2-223−23−23231-1-1100000000−2i32i3−333−3−3i3i3i−3ii3−i3−i3i3000000000000000000000000000000
χ704-4-44400-4-4400000000-2-22222-2-223−23−23231-1-11000000002i3−2i3−333−33i−3i−3i3i−i3i3i3−i3000000000000000000000000000000
χ714-4-44400-4-4400000000-2-22222-2-2−232323−231-1-1100000000−2i32i33−3−333i−3i−3i3ii3−i3−i3i3000000000000000000000000000000
χ724-4-44400-4-4400000000-2-22222-2-2−232323−231-1-11000000002i3−2i33−3−33−3i3i3i−3i−i3i3i3−i3000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000002202000200000000-100-1-1-100
χ746666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000-2-20-2000-20000000010011100
χ756666-366-3-3-3-6-6-3-33333000000000000000000000000000000000000000000002-20-2000200000000-100-11100
χ766666-366-3-3-3-6-6-3-3333300000000000000000000000000000000000000000000-2202000-2000000001001-1-100
χ776666-3-6-6-3-3-36-633-3-33300000000000000000000000000000000000000000000220-2000-200000000-1001-1100
χ786666-3-6-6-3-3-36-633-3-33300000000000000000000000000000000000000000000-2-202000200000000100-11-100
χ796666-3-6-6-3-3-3-663333-3-3000000000000000000000000000000000000000000002-202000-200000000-10011-100
χ806666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000000-220-2000200000000100-1-1100
χ811212-12-12-6006-6600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6006-66000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-6000063−630000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-60000−63630000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).